Application of Response Surface Method for Optimal Transfer Conditions of MLCC Alignment System

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1 Application of Response Surface Method for Optimal Transfer Conditions of MLCC System Su Seong Park Jae Min Kim Won Jee Chung Mechanical Design & Manufacturing Engineering, Changwon National University Changwon, , South Korea Tel: , 53-3 Fax: And O Chul Shin Solomon Mechanics Inc. Changwon, Kyongnam , South Korea ABSTRACT This paper presents the Application of Response Surface Method for Optimal Transfer Conditions of MLCC System. his paper is composed of two parts: (1) Testing performance verification of MLCC alignment system, compared with manual operation; (2) Applying response surface method to figuring out the optimal transfer conditions of MLCC transfer system. As a result testing performance verification of MLCC alignment system, the average alignment rates are 95% for 3216 chip, 88.5% for 2012 chip and 90.8% for 3818 chip. The MLCC alignment system can be accepted for practical use because average manual alignment is just 80%. In other words, the developed MLCC alignment system has been upgraded to a great extent, compared to manual alignment. Based on the successfully developed MLCC alignment system, the optimal transfer conditions have been explored by using RSM. The simulations using ADAMS has been performed according to the cube model of CCD. By using MiniTAB, we have established the model of response surface based on the simulation results. The optimal conditions resulted from the response optimization tool of MiniTAB has been verified by being assigned to the prototype of MLCC alignment system. Keywords: Multi-Layer Ceramic Capacitor (MLCC), system, Response Surface Method (RSM), MiniTAB, ADAMS 1. Introduction Nowadays cellular phones, digital cameras and MP3 s have been daily necessaries so that they become more compact and even lighter with powerful functions as days elapse. To cope with these demands, the electronic parts such as capacitors are much smaller. For this purpose, a new type of capacitor, called as Multi-Layer Ceramic Capacitor (abbreviated as MLCC), is shown up. The MLCC can allow an electronic product to be ultra-light. Accordingly, the demand of MLCC is consistently increasing. In turn, this pushes up the automation for producing MLCC s efficiently. This is why we are getting into research for MLCC production automation system with Solomon Mechanics Inc. However, the interprocess automation, i.e., automation between two neighboring processes, is lower than the automation of each process. In this paper, the MLCC alignment system which aims at the inter-process automation between the first and the second firing processes will be dealt with. In specific, without the MLCC alignment system, manual process would intervene for the inter-process between above two processes. Figure 1 shows the MLCC alignment system developed by Solomon Mechanics Inc. This paper is composed of two parts: (1) Testing performance verification of MLCC alignment system, compared with manual operation; (2) Applying response surface method to figuring out the optimal transfer conditions of MLCC transfer system.

chips, iii) conveyor unit for transferring chips from the feeding part to weight measuring part, iv) aligning part of chips, and v) transferring part of chips.

2 2. Testing performance verification of MLCC alignment system 2.1 MLCC alignment system Fig. 2 Schematic of MLCC System Fig. 1 MLCC System The MLCC alignment system from the 1 st firing process to the 2 nd firing process can be outlined as follows: i) the feeding part of the 1 st fired chips, ii) weight measuring part of chips, iii) conveyor unit for transferring chips from the feeding part to weight measuring part, iv) aligning part of chips, and v) transferring part of chips. M L C C Table 1 Testing chips of MLCC Items Conditions Model Size(LWH) 3.2*1.6* *1.2* *1.8*1.8 Area(cm 3 /EA) Weight(g/EA) Cycle time 8 s In order to verify the performance of MLCC alignment system, we have conducted some experiments by using various testing chips. The model numbers of MLCC are 3216, 2012 and 3818, whose size, area and weight are listed in Table 1. In Table 2, the alignment reference is shown for testing chips. In specific, GOOD decision of alignment will be made when 90% quantity or 90% weight can be obtained. Especially the initial operating conditions for the MLCC alignment system is shown in Table 3. Here Vel1 denotes the forward velocity of a feeder (of MLCC alignment system), while Vel2 denotes the return velocity of a feeder. In the meanwhile, Length indicates the transfer distance of a feeder.[1] The principle of MLCC alignment system can be briefly explained as follows. The chips of MLCC are dropped freely under gravitation from a chute as shown in Fig. 2. Then Vel1 would make chips move forward by not exceeding a static friction between each chip and feeder floor, whereas Vel2 would make chips move back by exceeding the static friction. Consequently this kind of iterating motion can result in the vibration which can further induce alignment. It can be noted that the rugged terrains in Fig. 2 will play an important role in alignment, by incorporating the vibrating floor of feeder. Table 2 Reference for Testing chips (EA) Weight(g) MLCC 100% 90% 100% 90% ,688 4, ,000 9, ,428 3, Table 3 Initial factors Vel1(m/s) Vel2 (m/s) Length (mm) Initial factors Result of testing performance verification For each chip, 10 experiments have been made as shown in Table 3. The average alignment quantities and rates are 4,453/95% for 3216 chip, 8,853/88.5% for 2012 chip and 3,119/90.8% for 3818 chip. Even though 2012 chip has reached 88.5% in alignment rate below than 90% of GOOD alignment, the MLCC alignment system can be accepted for practical use because average manual alignment is just 80%. In other words, the developed MLCC alignment system has been upgraded to a great extent, compared to manual alignment.

Table 4 Results of Testing Experiments Class 3216 2012 3818 Test 1 4,439 94.7 8,829 88.3 3,098 90.3 2 4,491 95.8 8,843 88.4 3,122 91.0 3 4,439 94.7 8,858 88.6 3,106 90.5 4 4,467 95.3 8,877 88.

3 Table 4 Results of Testing Experiments Class Test 1 4, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Average 4, , , RSM 3. RSM and Optimum conditions Based on the successfully developed MLCC alignment system, the optimal transfer conditions will be explored by using Response Surface Method [2] (abbreviated as RSM). In specific, RSM is used for finding the optimal values of 3 design factors (or variables) Vel1, Vel2 and Length for chip feeding motion of the developed MLCC alignment system. By using ADAMS [3], we have simulated 30 chips of 3216 chip. The CCD has added axial and center points the 2 k factorial design in order to estimate the change of design variables according to the level changes of response variables which would be resulted from less simulations or experiments. The CCD is composed of cube model and axial model. In this paper, the cube model of CCD is used as shown in Table 5. Figure 4 shows one of the simulation results using ADAMS according to the design of experiment shown in Table 7. Table 6 shows the range (especially lower and upper bounds) of design variables for CCD. Here α for CCD is usually chosen to maintain rotatability in indicating the distance between the center Table 5 Cube Model of CCD Cube points 8 Center points in cube 6 Axial point 6 Center points in axial 1 α 1.68 Table 6 Range of Design Variables Design variable Lower Upper Vel1(m/s) Vel2 (m/s) Length (mm) Each chip has been constrained by the contact condition which can realize colliding effects between each other. For each simulation, the elapse time of transferring chips is set as 8 s, the same as the practical operation of the developed MLCC alignment system. The simulation resolution is set as 900 steps. The flowchart of RSM is summarized in Fig. 3. Plan response surface method Execute computational analysis Analyze response surface Optimize response optimization Execute verification analysis Fig. 3 Flowchart for response surface method The response surface method with the Central Composite Design (abbreviated as CCD) method [4] is used to approximate a response variable (i.e., transfer credit in this paper). In the CCD method, each design variable can be selected by using MiniTAB [5], only considering the lower and upper bounds. In addition, total 20 ADAMS simulations (2 3 +2*3+6=20) are performed with 3 design variables as shown in Table Result of RSM Fig. 4 Simulation of ADAMS In Table 7, Transfer Credit indicates the performance index for each set of design variables (or operating conditions), i.e., Vel1, Vel2 and Length. In the simulation of ADAMS, each chip can get 4 Transfer Credits when it can pass over 4 specified (rugged) terrains (which are needed for alignment of chips) as shown in Fig. 4. Actually when each chip should pass over the first terrain, it can have 1 Transfer Credit. It follows that the full Transfer Credit is 120 when 30 chips can pass over 4 terrains in 8 seconds.

Table 7 Simulation Result No. Vel1 Vel2 Length Transfer Credit 1 0.0050000 0.0600000 6.00000 28 2 0.0251134 0.0450000 4.50000 0 3 0.0050000 0.0600000 3.00000 0 4 0.0125000 0.0197731 4.50000 0 5 0.

4 Table 7 Simulation Result No. Vel1 Vel2 Length Transfer Credit It can be noticed that Transfer Credit can have 0. This can be explained as follows. In simulation, only 30 chips are simulated rather than actual number of some thousands chips. In practice, a lot of chips can result in the interaction (between each other) which could push chips over 4 rugged terrains. Thus the interaction effect of only 30 chips can be much lower than that of some thousands chips. This can make Transfer Credit 0. In addition, the reason why only 30 chips are selected as a simulation model is that its simulation time in ADAMS is about one and half hour for each simulation. The total simulation time amounts to 30 hours for 20 cases. selected regression model has been made. When the selected model cannot be compatible, the response surface model can be reduced by pooling the terms which are not significant at the table of variance analysis. Through this process, a final regression model can be re-established. Figure 5 shows the final model of response surface regression. In specific, for any model of response surface, the value of P for each term has been checked. Then from the largest P value, once one term can be made pooling so that a model can be fitted. After fitting, R-sq and lackof-fit can be confirmed in Fig. 5 and Table 8, respectively. As a result, it follows that Vel1*Vel2, Vel2*Length and Vel2*Length are not significant, which in turn are ruled out by pooling as shown in Fig. 5.[6] Fig. 5 Final Model of Response Surface Regression In order to evaluate the compatibility of surface regression model, both residual analysis and analysis of variance (i.e., ANOVA) are used. Figure 6 shows normal probability plot of the residuals. In this figure, the final model of surface regression is in good accordance with normal distribution. By using MiniTAB, we have established the model of response surface based on the simulation results according to CCD. Especially a quadratic polynomial model has been estimated by using model fitting. For both the construction of response surface and the estimation of regression equation, a full quadratic form of estimation model has been established by considering response surface forms for all the design variables. Then by using residual analysis, lack-of-fit, and the coefficient of determination, decision on the compatibility of Fig. 6 Normal probability plot of the residuals for Transfer Credit

Table 8 shows ANOVA table for Transfer Credit. It can be noticed that the final model of surface regression is turned out to be compatible since lack-of-fit of 0.114 is greater than 0.05 (95%).

5 Table 8 shows ANOVA table for Transfer Credit. It can be noticed that the final model of surface regression is turned out to be compatible since lack-of-fit of is greater than 0.05 (95%). Besides, the coefficient of determination (i.e., R-sq) of 95.2% denotes that the final model of regression surface is valid. Table 8 ANOVA Table for Transfer Credit Source DF Seq SS Adj SS Adj MS F P Regression Fig. 7 Optimal Conditions resulted from MiniTAB Linear Square Interaction Residual Error Lack of fit Pure Error Total Based on the results of analyses, Transfer Credit, T, (which denotes the performance of chip transfer according to Vel1, Vel2, and Length in ADAMS simulations) can be obtained in a form of quadratic polynomial as follows: 4. Application to Prototype of MLCC System The optimal conditions, Vel1 = 0.019, Vel2 = , Length = , resulted from the response optimization tool of MiniTAB has been verified by being assigned to the prototype of MLCC alignment system shown in Fig. 1. Especially the operation result of MLCC alignment system using the initial conditions (Vel1 = 0.015, Vel2 = 0.043, Length = 4.000) is compared with that of MLCC alignment system using the optimal conditions as shown in Fig. 8. It can be noticed that the alignment rate using the optimal conditions has been increased by 1.5%, compared to the case of operation using the initial conditions for 3216 chip (see Table 9). (1) where T, V 1, V 2, and L denote Transfer Credit, Vel1, Vel2, Length, respectively. 3.3 Optimum conditions In order to figure out the optimal transfer conditions of Vel1, Vel2, and Length, the tool of response optimization in MiniTAB has been used based on equation (1). As mentioned before, this optimization seeks for Larger-thebetter characteristics since the response variable, i.e., Transfer Credit, would be better if it could be close to the full credit of 120. Under the constraint of 110 Transfer Credit 120, the optimal transfer conditions satisfying Larger-the-better characteristics, are Vel1 = 0.019, Vel2 = , Length = as shown in Fig. 7. Table 9 Comparison of Operations using Initial and Optimal Conditions 3216(optimal Class 3216(Initial conditions) conditions) Test 1 4, , , , , , , , , , Average 4,

6 References [1] O. C. Shin, S. H. Jung, S. R. Jung, W. J. Jung, J. M. Kim, [2] Song, C. G., Jo, B. G., MSC.ADAMS For multibody dynamics analysis ", 2007 [3] W.C. Kim, J. J. Kim, B. W. Park, S. H. Park, T. S. Park, M. S. Song, S. Y. Lee, Y. J. Lee, J. W. Jeon, S. S. Cho, Introduction to Statistics pp , 2005 [4] Myers, R. H, and Montgomery, D. C. Response surface Methodology John wiley & Sons Inc. New York, [5] S. B. Lee, Minitab User Handbook, 2002 [6] Jung, D.W. Chung, W.J. Kim, H.C. Bang, Y.M. Yoon, Y.M. Six Sigma Robust Design of Fork Park for LCD Transfer System WMSCI, Fig. 8 Results of Operations for Prototype of MLCC System using Initial and Optimal Conditions 5. Conclusion In conclusion, based on the successfully developed MLCC alignment system, the optimal transfer conditions have been explored by using RSM. The RSM with CCD method has been used to approximate a response variable, i.e., Transfer Credit. The simulations using ADAMS has been performed according to the cube model of CCD. By using MiniTAB, we have established the model of response surface based on the simulation results. In order to evaluate the compatibility of surface regression model, both residual analysis and analysis of variance have been used to show that the final model of surface regression is in good accordance with normal distribution. Based on the results of analyses, the performance of chip transfer has been obtained in a form of quadratic polynomial, given by equation (1). The optimal conditions resulted from the response optimization tool of MiniTAB has been verified by being assigned to the prototype of MLCC alignment system. It was shown that the alignment rate using the optimal conditions has been increased by 1.5%, compared to the case of operation using the initial conditions. Acknowledgement This work was partially supported (in part) by the Solomon Mechanics Inc.

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